Past projects

Figure 1: An unstable flow configuration. The radial component of the velocity was perturbed in the transition layer. The vertical component of the magnetic field is shown in color, arrows represent the perturbation velocity field (initial velocity field is subtracted). The eigen mode with the azimuthal wavenumber m=3 is growing. Onset of the Kelvin-Helmholtz instability of an axisymmetric flux tube in a vortex flow.

Magnetic flux concentrations in the solar (sub)photosphere are surrounded by strong downflows, which come into swirling motion owing to the conservation of angular momentum. While such a whirl flow can stabilize a magnetic flux tube against the MHD fluting instability, it potentially becomes subject to the Kelvin-Helmholtz and shear instabilities near the edge of the flux tube, which may lead to twisting of the magnetic field and perhaps even to the disruption of the magnetic structure. As a first step towards studying the relevance of such instabilities, we investigate the stability of an incompressible flow with longitudinal and azimuthal (whirl) components surrounding a cylinder with a uniform longitudinal magnetic field. We find that a sharp jump of the azimuthal flow component at the cylinder boundary always leads to a Kelvin-Helmholtz-type instability for sufficiently small wavelengths of the perturbation. On the other hand, a smooth and wide enough transition of the azimuthal velocity towards the surface of the cylinder leads to stable configurations, even for a discontinuous profile of the longitudinal flow.

Helicity fluctuations in a mean-field dynamo model lead to a secular variation of the dipole moment and occasionally to sudden polarity reversals. The fluctuations perturb the fundamental dynamo mode, a non-oscillatory dipole, and excite higher modes. This results in stochastic oscillations of the dipole field amplitude in a bistable potential with minima representing normal and reversed polarity, and occasional jumps between them. A relation between the intensity variation and the reversal rate is found, and the observed amplitude distribution of the dipole field is reproduced. The figure displays the toroidal magnetic field as a function of colatitude and time (in units of the diffusion time) with red and blue indicating the two polarities. In the lower panel the dipole amplitude is plotted versus time.

Large scale magnetic fields in the Earth and other planets, in the Sun and other active stars and also in spiral galaxies are apparently maintained by hydromagnetic dynamos. Concerning the geodynamo there are now dynamo models available that reproduce many features of the Earth's magnetic field very successfully without making any use of mean-field theory. One aim of our work is to compare these results with those based on mean-field theory. This will give an estimation on the reliability and validity of mean-field theory which still is used in dynamo models for various astronomical objects. Within mean-field models the mean-field coefficients a and b are decisive quantities in order to describe dynamo action. We use a dynamically computed velocity field with the aim to calculate mean-field coefficients for the earth's outer core. The 9 components of an a-tensor are shown in the figure on the left. In the other figure, a comparison between direct numerical simualtions and mean-field calculations is presented. While a mean-field model which relies on the full set of determined mean-field coefficients (right, second row) reproduces the azimuthally averaged field given by a direct numerical simulation (right, first row) in great detail, an isotropic approximation for a and b (right, last row) leads to deviations in the amplitudes of the poloidal field and to a different field topology of the induced toroidal field.

References